surface area can calculus problem?
hi. i would like to find out how to solve this problem.
You have been asked to design a can shaped like a right circular cylinder with height h and radius r. Given that the can must hold exactly 810 cm^3, what values of h and r will minimise the total surface area (including the top and bottom faces)?
The answers should be correct to 2 decimal places as a list [in brackets] of the form: [ h, r ]
for constants h (height), r (radius), in that order.
cm^3 means cubic centimetres
thanks for any help. it is very much appreciated
I’d take the derivative of the SA. This will give you either a min or a max. But first, I would try to solve SA to be in terms of just one variable.
Let’s now take a derivative of SA with respect to r.
When this equals zero, we have a min or a max.
I’m going to multiply everything by r^2.
Using our original equation, we now solve for h:
Calculus Area Problem Part IV: The Conclusion of the Area Problem